Module etm
A pure Python version of Karney's Exact Transverse
Mercator (ETM) projection.
Classes Etm,
ETMError and
ExactTransverseMercator, transcoded from Karney's
C++ class TransverseMercatorExact, abbreviated as
TMExact below.
Class ExactTransverseMercator provides Exact Transverse
Mercator projections while instances of class Etm represent ETM
(easting, northing) locations. See also Karney's
utility TransverseMercatorProj and use "python[3] -m
pygeodesy.etm ..." to compare the results.
Following is a copy of Karney's TransverseMercatorExact.hpp file
Header.
Copyright (C) Charles Karney (2008-2023) and licensed under the
MIT/X11 License. For more information, see the GeographicLib documentation.
The method entails using the Thompson Transverse Mercator as an intermediate
projection. The projections from the intermediate coordinates to
phi, lam and x, y are given by elliptic
functions. The inverse of these projections are found by Newton's method
with a suitable starting guess.
The relevant section of L.P. Lee's paper Conformal Projections Based On Jacobian Elliptic
Functions in part V, pp 67-101. The C++ implementation and notation
closely follow Lee, with the following exceptions:
Lee here Description
x/a xi Northing (unit Earth)
y/a eta Easting (unit Earth)
s/a sigma xi + i * eta
y x Easting
x y Northing
k e Eccentricity
k^2 mu Elliptic function parameter
k'^2 mv Elliptic function complementary parameter
m k Scale
zeta zeta Complex longitude = Mercator = chi in paper
s sigma Complex GK = zeta in paper
Minor alterations have been made in some of Lee's expressions in an
attempt to control round-off. For example, atanh(sin(phi))
is replaced by asinh(tan(phi)) which maintains accuracy near
phi = pi/2. Such changes are noted in the code.
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parseETM5(strUTM,
datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran...,
Etm=<class 'pygeodesy.etm.Etm'>,
falsed=True,
name='')
Parse a string representing a UTM coordinate, consisting of
"zone[band] hemisphere easting northing". |
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toEtm8(latlon,
lon=None,
datum=None,
Etm=<class 'pygeodesy.etm.Etm'>,
falsed=True,
name='',
strict=True,
zone=None,
**cmoff)
Convert a geodetic lat-/longitude to an ETM coordinate. |
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parseETM5 (strUTM,
datum=Datum(name='WGS84', ellipsoid=Ellipsoids.WGS84, transform=Tran...,
Etm=<class 'pygeodesy.etm.Etm'>,
falsed=True,
name='')
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Parse a string representing a UTM coordinate, consisting of
"zone[band] hemisphere easting northing".
- Arguments:
strUTM - A UTM coordinate (str).datum - Optional datum to use (Datum,
Ellipsoid, Ellipsoid2 or a_f2Tuple).Etm - Optional class to return the UTM coordinate (Etm) or
None.falsed - Both easting and northing are falsed
(bool).name - Optional Etm name (str). - Returns:
- The UTM coordinate (
Etm) or if
Etm is None, a UtmUps5Tuple(zone, hemipole, easting,
northing, band). The hemipole is the
hemisphere 'N'|'S'.
- Raises:
ETMError - Invalid strUTM.TypeError - Invalid or near-spherical datum.
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toEtm8 (latlon,
lon=None,
datum=None,
Etm=<class 'pygeodesy.etm.Etm'>,
falsed=True,
name='',
strict=True,
zone=None,
**cmoff)
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Convert a geodetic lat-/longitude to an ETM coordinate.
- Arguments:
latlon - Latitude (degrees) or an (ellipsoidal) geodetic
LatLon instance.lon - Optional longitude (degrees) or None.datum - Optional datum for the ETM coordinate, overriding
latlon's datum (Datum,
Ellipsoid, Ellipsoid2 or a_f2Tuple).Etm - Optional class to return the ETM coordinate (Etm) or
None.falsed - False both easting and northing (bool).name - Optional Utm name (str).strict - Restrict lat to UTM ranges
(bool).zone - Optional UTM zone to enforce (int or
str).cmoff - DEPRECATED, use falsed. Offset longitude
from the zone's central meridian (bool). - Returns:
- The ETM coordinate as an
Etm instance or a UtmUps8Tuple(zone, hemipole, easting,
northing, band, datum, gamma, scale) if
Etm is None or not
falsed. The hemipole is the
'N'|'S' hemisphere.
- Raises:
ETMError - No convergence transforming to ETM easting and northing.ETMError - Invalid zone or near-spherical or incompatible
datum or ellipsoid.RangeError - If lat outside the valid UTM bands or if
lat or lon outside the
valid range and pygeodesy.rangerrors set to True.TypeError - Invalid or near-spherical datum or
latlon not ellipsoidal.ValueError - The lon value is missing or
latlon is invalid.
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